Guided Worksheet Formal Definition of Limit: An Instrument Development Process

Rina Oktaviyanthi; Ria Noviana Agus

doi:10.35445/alishlah.v13i1.483

Guided Worksheet Formal Definition of Limit: An Instrument Development Process

Rina Oktaviyanthi, Ria Noviana Agus

Abstract

This study aims to develop a guided worksheet to fulfil the needs of students to understand the formal concept of Limit. This was carried out using a developmental study that focuses on content analysis and expert review through substantial analysis, structural design, prototype development and evaluation. The research sample was 95 first-year students, especially those in engineering and science majors who enrolled in Calculus. The data process of instrument development, the data of expert validation, and the data of limited trial were produced in this research. To assess all the research data applied the Q-Cochran and the Cronbach Alpha statistical test. The results are a guided worksheet for limit evaluation in visual form with schematic design and scaffolding or framework type. Expert testing and limited testing showed Asymp.Sig. = 0,088 > 0,05 and r_coefficient = 0,382 > r_critical = 0,2017. It indicates that the items composing this guided worksheet are valid and reliable therefore, they can be used to solve student difficulties related to the formal rules of Limit.

Keywords

Content analysis; development research; formal definition of limit; formal worksheet of limit; guided worksheet

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References

Akbar, S. D. (2013). Instrumen perangkat pembelajaran. Bandung: PT Remaja Rosdakarya.

Albano, G., & Iacono, U. D. (2019). A scaffolding toolkit to foster argumentation and proofs in mathematics: some case studies. International Journal of Educational Technology in Higher Education, 16(1), 1-12. https://doi.org/10.1186/s41239-019-0134-5

Alsina, A., Maurandi, A., Ferre, E., & Coronata, C. (2021). Validating an Instrument to Evaluate the Teaching of Mathematics Through Processes. International Journal of Science and Mathematics Education, 19(3), 559-577. https://doi.org/10.1007/s10763-020-10064-y

Ashraf, A. L. A. M. (2020). Challenges and Possibilities in Teaching and Learning of Calculus: A Case Study of India. Journal for the Education of Gifted Young Scientists, 8(1), 407-433. https://doi.org/10.17478/jegys.660201

Ayalon, M., & Wilkie, K. J. (2020). Developing assessment literacy through approximations of practice: Exploring secondary mathematics pre-service teachers developing criteria for a rich quadratics task. Teaching and Teacher Education, 89, 103011. https://doi.org/10.1016/j.tate.2019.103011

Bakhy, S., Kalimbetov, B., & Khabibullayev, Z. (2018). Possibilities of mathematical problems in logical thinking. Development of secondary education pupils. Opción: Revista de Ciencias Humanas y Sociales, (85), 441-457.

Barniol, P., & Zavala, G. (2016). A tutorial worksheet to help students develop the ability to interpret the dot product as a projection. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2387-2398. https://doi.org/10.12973/eurasia.2016.1271a

Butcher, C., Davies, C., & Highton, M. (2019). Designing learning: from module outline to effective teaching. Routledge.

Cohen, L., Manion, L., & Morrison, K. (2017). Research methods in education. routledge.

Dagoc, D., & Tan, D. A. (2018). Effects of metacognitive scaffolding on the mathematics performance of grade 6 pupils in a cooperative learning environment. International Journal of English and Education, 7(4), 378-391.

Dasaprawira, M. N., Zulkardi, & Susanti, E. (2019). Developing Mathematics Questions of PISA Type Using Bangka Context. Journal on Mathematics Education, 10(2), 303-314. https://doi.org/10.22342/jme.10.2.5366.303-314

Dibbs, R. (2019). Forged in failure: engagement patterns for successful students repeating calculus. Educational Studies in Mathematics, 101(1), 35-50. https://doi.org/10.1007/s10649-019-9877-0

Flórez, R., & Mukherjee, A. (2020). Classroom Experiences in Introducing Students to Conjectures, Exploration and Visual Proofs Using Experiments on the Möbius Strip. PRIMUS, 30(1), 50-66. https://doi.org/10.1080/10511970.2018.1506530

Guzey, S. S., Harwell, M., & Moore, T. (2014). Development of an instrument to assess attitudes toward science, technology, engineering, and mathematics (STEM). School Science and Mathematics, 114(6), 271-279. https://doi.org/10.1111/ssm.12077

Hagman, J. E., Johnson, E., & Fosdick, B. K. (2017). Factors contributing to students and instructors experiencing a lack of time in college calculus. International journal of STEM education, 4(1), 1-15. https://doi.org/10.1186/s40594-017-0070-7

Hanna, G. (2020). Mathematical proof, argumentation, and reasoning. Encyclopedia of mathematics education, 561-566. https://doi.org/10.1007/s10649-021-10046-z

Kahl, W. (2020). Calculational relation-algebraic proofs in the teaching tool CalcCheck. Journal of Logical and Algebraic Methods in Programming, 117, 100581. https://doi.org/10.1016/j.jlamp.2020.100581

Katrancı, M. (2015). Book reading motivation scale: Reliability and validity study. Educational Research and Reviews, 10(3), 300-307. https://doi.org/10.5897/ERR2014.1998

Keh, H. T., & Sun, J. (2018). The differential effects of online peer review and expert review on service evaluations: the roles of confidence and information convergence. Journal of Service Research, 21(4), 474-489. https://doi.org/10.1177/1094670518779456

Kilic, H. (2018). Pre-service mathematics teachers’ noticing skills and scaffolding practices. International Journal of Science and Mathematics Education, 16(2), 377-400. https://doi.org/10.1007/s10763-020-10101-w

Kumar, R. (2018). Research methodology: A step-by-step guide for beginners. Sage.

Krosnick, J. A. (2018). Questionnaire design. In The Palgrave handbook of survey research (pp. 439-455). Palgrave Macmillan, Cham.

Ingram, N., Holmes, M., Linsell, C., Livy, S., McCormick, M., & Sullivan, P. (2019). Exploring an innovative approach to teaching mathematics through the use of challenging tasks: a New Zealand perspective. Mathematics Education Research Journal, 1-26. https://doi.org/10.1007/s13394-019-00266-1

Japkowicz, N., & Shah, M. (2011). Evaluating learning algorithms: a classification perspective. Cambridge University Press.

Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424. https://doi.org/10.1016/j.ijer.2019.04.002

Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. Zdm, 49(6), 937-949. https://doi.org/10.1007/s11858-017-0867-3

Luthfiana, A., Ambarita, A., & Suwarjo, S. (2018). Developing worksheet based on multiple intelligences to optimize the creative thinking students. JIPM (Jurnal Ilmiah Pendidikan Matematika), 7(1), 1-12. http://doi.org/10.25273/jipm.v7i1.2430

Mohajan, H. K. (2017). Two criteria for good measurements in research: Validity and reliability. Annals of Spiru Haret University. Economic Series, 17(4), 59-82. https://10.26458/1746

Nasrullah, A., Marlina, M., & Dwiyanti, W. (2018). Development of Student Worksheet-Based College E-Learning Through Edmodo to Maximize the Results of Learning and Motivation in Economic Mathematics Learning. International Journal of Emerging Technologies in Learning, 13(12). https://doi.org/10.3991/ijet.v13i12.8636

Oktaviyanthi, R., Herman, T., & Dahlan, J. A. (2018). How Does Pre-Service Mathematics Teacher Prove the Limit of a Function by Formal Definition?. Journal on Mathematics Education, 9(2), 195-212. https://doi.org/10.22342/jme.9.2.5684.195-212

Oktaviyanthi, R., & Dahlan, J. A. (2018, April). Developing guided worksheet for cognitive apprenticeship approach in teaching formal definition of the limit of a function. In IOP Conference Series: Materials Science and Engineering (Vol. 335, No. 1, p. 012120). IOP Publishing. https://doi.org/10.1088/1757-899X/335/1/012120

Oktaviyanthi, R., & Agus, R. N. (2020). Instrumen Evaluasi Kemampuan Penalaran Adaptif Matematis Mahasiswa. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(4). http://dx.doi.org/10.24127/ajpm.v9i4.3150

Richard, P. R., Venant, F., & Gagnon, M. (2019). Issues and challenges in instrumental proof. In Proof Technology in Mathematics Research and Teaching (pp. 139-172). Springer, Cham. https://doi.org/10.1007/978-3-030-28483-1_7

Richey, R. C., Klein, J. D., & Tracey, M. W. (2010). The instructional design knowledge base: Theory, research, and practice. Routledge.

Rocha, H. (2019). Mathematical proof: from mathematics to school mathematics. Philosophical Transactions of the Royal Society A, 377(2140), 20180045. https://doi.org/10.1098/rsta.2018.0045

Schoenfield, M. (2018). An accuracy based approach to higher order evidence. Philosophy and Phenomenological Research, 96(3), 690-715. https://doi.org/10.1111/phpr.12329

Spivak, M. (2018). Calculus on manifolds: a modern approach to classical theorems of advanced calculus. CRC press.

Tracy, S. J. (2019). Qualitative research methods: Collecting evidence, crafting analysis, communicating impact. John Wiley & Sons.

van der Scheer, E. A., Bijlsma, H. J., & Glas, C. A. (2019). Validity and reliability of student perceptions of teaching quality in primary education. School effectiveness and school improvement, 30(1), 30-50. https://doi.org/10.1080/09243453.2018.1539015

DOI: https://doi.org/10.35445/alishlah.v13i1.483